An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For helium-like ions, in particular, we propose to measure either the angular distribution or polarization of the $1s2p~^{ 3}P_{ 1}, F \rightarrow 1s^{ 2}~^{ 1}S_{ 0}, F_{ f}$ emission following the stimulated decay of the initial $1s2s~^{ 1}S_{ 0}, F_{ i}$ level. It is found that both the angular and polarization characteristics of the emitted x-ray photons strongly depends on the (relative) \textit{ splitting} of the partially overlapping hyperfine $1s2p~^{ 3}P_{ 1}, F$ resonances and may thus help resolve their hyperfine structure. The proposed scheme is feasible with present-day photon detectors and allows a measurement of the hyperfine splitting of helium-like ions with a relative accuracy of about $10^{ -4}$.
Categories: physics.atom-ph